{
  "id": "1402.0169",
  "version": "v1",
  "published": "2014-02-02T10:05:44.000Z",
  "updated": "2014-02-02T10:05:44.000Z",
  "title": "$a$-Points of the Riemann zeta-function on the critical line",
  "authors": [
    "S. J. Lester"
  ],
  "comment": "20 pages, To appear in Int. Math. Res. Notices",
  "doi": "10.1093/imrn/rnt356",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the proportion of the nontrivial roots of the equation $\\zeta (s)=a$, which lie on the line $\\Re s=1/2$ for $a \\in \\mathbb C$ not equal to zero. We show that at most one-half of these points lie on the line $\\Re s=1/2$. Moreover, assuming a spacing condition on the ordinates of zeros of the Riemann zeta-function, we prove that zero percent of the nontrivial solutions to $\\zeta (s)=a$ lie on the line $\\Re s=1/2$ for any nonzero complex number $a$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-02T10:05:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "60F05"
    ],
    "keywords": [
      "riemann zeta-function",
      "critical line",
      "nonzero complex number",
      "nontrivial roots",
      "points lie"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.0169L"
    }
  }
}